Aristotle's physics Carlo Rovelli Aix Marseille Universit´e,CNRS, CPT, UMR 7332, 13288 Marseille, France. Universit´ede Toulon, CNRS, CPT, UMR 7332, 83957 La Garde, France. (Dated: December 14, 2013) I show that Aristotelian physics is a correct approximation of Newtonian physics in its appropriate domain, in the same precise sense in which Newton theory is an approximation of Einstein's theory. Aristotelian physics lasted long not because it became dogma, but because it is a very good theory. I. INTRODUCTION Aristotle's physics [1{3] does not enjoy good press. It is commonly called \intuitive", and blatantly wrong. For instance, it states that heaver objects fall faster, when every high-school kid learns they fall at the same speed. Science, we read, established itself by escaping the Aristotelian straightjacket and learning to rely on observation. Aristotelian physics is not even covered in the numerous entries of the Stanford Encyclopaedia of Philosophy devoted to Aristotle [4]. Here is a typical example of evaluation: \Traditionally scholars have found the notion congenial that Aristotle's intended method in his works on natural science is empirical, even as they have criticized him for failures on this count. The current generation has reversed this verdict entirely. The Physics in particular is now standardly taken as a paradigm of Aristotle's use of dialectical method, understood as a largely conceptual or a priori technique of inquiry appropriate for philosophy, as opposed to the more empirical inquiries which we, these days, now typically regard as scientific”[5]. That is, Aristotle's science is either not science at all, or, to the extent it is science, it is failure. I think that this view of Aristotle's physics is wrong. Aristotle's physics is counterintuitive, based on observation, and correct (in its domain of validity) in the same sense in which Newtonian physics is correct (in its domain). Newtonian physics provides a conceptual scheme for understanding physical phenomena and an effective technical tool. But strictly speaking it is wrong. For instance, the planet Mercury follows an orbit which is not the orbit predicted by Newtonian physics. Einstein's theory provides a description of gravitational phenomena that predicts the observed motion of Mercury. Newtonian theory matches Einstein's theory in a domain of phenomena which include most of our experience, but our observational precision on Mercury is sufficient to reveal the discrepancy. This limitation does not compromise the value {practical, conceptual and historical{ of Newton theory, which remains the rock on which Einstein built, and an extraordinary useful theory of the world around us. The relation between Einstein's and Newton's theories is detailed in all relativity manuals: if we restrict Einstein's theory to a certain domain of phenomena (small relative velocities, weak gravitational field...), in the appropriate approximation we obtain Newton theory. Understanding this relation is not an empty academical exercise: it is an important piece of theoretical physics in the cultural baggage of a good scientist. It clarifies what is the meaning of the domain of validity of a theory and it sheds light on the very nature of physical theories: we already know, indeed, that Einstein's theory, in turn, has limited domain of validity (it is invalid beyond the Planck scale). I show in this note that the technical relation between Aristotle's physics and Newton's physics is of the same nature as the relation between Newton's physics and Einstein's physics. To this comparison I add some general considerations on the nature of scientific progress, in the last section. II. BRIEF REVIEW OF ARISTOTLE'S PHYSICS History of science can have two distinct objectives. The first is to reconstruct the historical complexity of an author or a period. The second is to understand how have we got to know what we know. There is tension between these two aims. Facts or ideas of scarce relevance for one may have major relevance for the other. Take the characteristic case of a scientist who has worked a large part of his life on a theory A, soon forgotten and without historical consequences, and for a short period on a theory B, which has opened the way to major later developments. The historian working from the first perspective is mostly interested in A and scarcely in B. The historian working from the second perspective is mostly interested in B and scarcely in A, because what matters to him is the way future has developed thanks to B. As a scientists of today, I respect the historians working within the first perspective, but I regret a trend that undervalues the second. If we want to understand the past we better disregard the future of that past, but if we want to understand the present we better not disregard the past steps that were essential for getting to the present. This is of importance especially for those of us engaged in trying to push ahead the scientific path of discovery today. We are not much interests in what scientists did wrong, there is too much of that. We are interested in what they did right. Because we are tying to copy them in this, not in that. 2 From this perspective, I take the liberty to summarize Aristotle's physics using a modern terminology whenever possible. Aristotle details his physics mostly in three books: \Physics" (below referred to as [Ph]) \On the Heavens" (below referred to as [He]) and \On Generation and Corruption". The first is the book that has given the name to the discipline; it is a profound masterpiece, it discusses Eleatism, the notion of change, the nature of motion, the infinite, space, time, infinite divisibility, and else [5{7]. Some of the issues discussed, such as the nature of Time, are still of central relevance today, for instance in quantum gravity research. But it is not on this which I focus here. The second is simpler and contains most of what we call Aristotle's physics today. I focus here on the parts of the theory that are comparable to Newtonian physics, and which form the basis of the Aristotelian theory of local movement (fora´). The theory is as follows. There are two kind of motions (a) Violent motion, or unnatural [Ph 254b10], (b) Natural motion [He 300a20] Violent motion is multiform and is caused by some accidental external agent. For instance a stone is moving towards the sky because I have thrown it. My throwing is the cause of the violent motion. Natural motion is the motion of objects left to themselves. Violent motion is of finite duration. That is: (c) Once the effect of the agent causing a violent motion is exhausted, the body comes to rest. To describe natural motion, on the other hand, we need a bit of cosmology. The cosmos is composed by mixtures of five elementary substances to which we can give the names Earth, Water, Air, Fire [He 312a30], and Ether. The ground on which we walk (the \Earth") is mostly composed of Earth and has approximate spherical shape. It is surrounded by a spherical shell of Water, called the \natural place of Water", then a spherical shell of Air, called \natural place of Air", then Fire, the \natural place of the Fire" [He 287a30]. All this is immersed in a further spherical shell [He 286b10] of Ether, called the Heaven, where the celestial bodies like Sun, Moon and stars move. The entire sphere is much larger than the size of the Earth, which is of the order of 400 thousand stadii [He 298a15] (a bit too much, but a correct order of magnitude estimate of the size of the Earth). The entire cosmos is finite and the outmost spherical shell rotates rapidly around the central Earth. Given this structure of the cosmos, we can now describe natural motion. This is of two different kinds, according to whether it is motion of the Ether, or motion of one of the four elements Earth, Water, Air and Fire. (d) The natural motion of the Ether in the Heavens is circular around the center [He 26915]. (e) The natural motion of Earth, Water, Air and Fire is vertical, directed towards the natural place of the substance [He 300b25]. This is the general scheme. More in detail, Aristotle discusses also the rate at which the natural motion happens. He states that (f) Heavier objects fall faster: their natural motion towards downwards happens faster [Ph 215a25, He 311a19-21]; (g) the same object falls faster in a less dense medium [Ph 215a25]. Quantitative precision is not very common in Aristotle, who is interested in the causal and qualitative aspects of phenomena. But in the text following [Ph 215a25], Aristotle uses a mathematical (geometrical) notation from which one can infer that he is actually saying with a certain technical precision that the speed v of fall is proportional to the weight W of the body and inversely proportional to the density ρ of the medium. In modern notation, W (h0) v ∼ c : (1) ρ where c is a constant. What one can deduce from Aristotle's discussion is indeed a bit weaker: essentially that the speed would go to infinity if the density of the fluid would go to zero. In modern (and now definitely very anachronistic) terms this could be formulated as W n (h) v ∼ c : (2) ρ with positive n. About the constant c, Aristotle says that (i) The shape of the body [...] accounts for their moving faster or slower [He 313a14]; that is, the constant c is depends on the shape of the body.